Re: Interpretation of Components for Splines
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Re: Interpretation of Components for Splines

On Thu, 29 Apr 1999, Peter M. Saama wrote:

> Hello:
Dear Peter,
> When we fit spl(t), and dev(day) in ASREML, the .asr file contains output
> that looks like this:
>    Source               Model  terms     Gamma                Component
> Compnt/StndErr
>   spl(time)                 18      18        6.65133
> 4.113614             1.41 P  
>   dev(time)               20        20       0.603323E-01
> 0.103056E-02      0.47 P  
> ...
> In the above table is 4.113614 a smoothing parameter or is it a variance
> component? Furthermore, in the above table, is 0.103056E-02 a parameter
> used in specification of the roughness penalty or is it a variance component?
The component for spl(time) is a variance component, but it controls the
amount of smoothing. If this component (actually the ratio gamma) tends 
to zero, the spline fit tends to a straight line, as it gets large the 
fit tends to interpolation. The additional variance component, ie 
dev(time), allows for the presence of group effects, and can only be 
fitted if there is replication at each (or most) time point. This is in 
line with the usual one-way random effects analysis where you would fit 
y~ mu !r group
in asreml to get correct analysis ie estimating both an error and between 
groups variance.

The usual roughness penalty that is described in most smoothing texts is 
actually lambda = 1/gamma(spl).

I hope this helps

best wishes

> > Respectfully,
> Peter M. Saama /
> --
> Asreml mailinglist archive:

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